Problem: What is the extraneous solution to these equations? $\dfrac{x^2}{x + 10} = \dfrac{100}{x + 10}$
Solution: Multiply both sides by $x + 10$ $ \dfrac{x^2}{x + 10} (x + 10) = \dfrac{100}{x + 10} (x + 10)$ $ x^2 = 100$ Subtract $100$ from both sides: $ x^2 - (100) = 100 - (100)$ $ x^2 - 100 = 0$ Factor the expression: $ (x + 10)(x - 10) = 0$ Therefore $x = -10$ or $x = 10$ At $x = -10$ , the denominator of the original expression is 0. Since the expression is undefined at $x = -10$, it is an extraneous solution.